Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that make all equations true.

Front

What is a solution to a system of equations?

Back

A pair of values (x, y) that satisfy all equations in the system.

Front

What does it mean if a system has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system has no solution?

Back

The lines are parallel and never intersect.

Front

What does it mean if a system has infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

How can you tell if two lines are parallel?

Back

They have the same slope but different y-intercepts.

Front

How can you tell if two lines are the same?

Back

They have the same slope and the same y-intercept.

Front

What is the slope-intercept form of a line?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.